A Continuum Model for Flocking: Obstacle Avoidance, Equilibrium, and Stability
A Continuum Model for Flocking: Obstacle Avoidance, Equilibrium, and Stability
Files
Publication or External Link
Date
2010
Authors
Mecholsky, Nicholas Alexander
Advisor
Ott, Edward
Antonsen, Jr., Thomas M
Antonsen, Jr., Thomas M
Citation
DRUM DOI
Abstract
The modeling and investigation of the dynamics and configurations of animal groups is a subject of growing attention. In this dissertation, we present a partial-differential-equation based continuum model of flocking and use it to investigate several properties of group dynamics and equilibrium.
We analyze the reaction of a flock to an obstacle or an attacking predator. We show that the flock response is in the form of density disturbances that resemble Mach cones whose configuration is determined by the anisotropic propagation of waves through the flock.
We investigate the effect of a flock `pressure' and pairwise repulsion on an equilibrium density distribution. We investigate both linear and nonlinear pressures, look at the convergence to a ‘cold’ (T → 0) equilibrium solution, and find regions of parameter space where different models produce the same equilibrium.
Finally, we analyze the stability of an equilibrium density distribution to long-wavelength perturbations. Analytic results for the stability of a constant density solution as well as stability regimes for constant density solutions to the equilibrium equations are presented.